Description of the magma package

This is a short description of the Magma code that imports the databases of all arc-transitive cubic graphs on up to 10000 vertices (Foster Census) and all cubic semisymmetric graphs on up to 10000 vertices.

Cubic arc-transitive graphs

• load "ImportFosterCensus.mgm";

  Requires also: FosterCensus10k.txt and FosterCensus10kplaces.txt

  Import the database of all cubic semisymmetric graphs on up to 10000 vertices into memory. The following magma function become available:

  • NumberOfCubicATgraphs(n);

    Returns the number of cubic arc-transitive graphs on order \(n\) vertice, for \(n \le 10000\).

  • CubicATgraph(n,k);

    Returns the k-th cubic arc-transitive graph on \(n\) vertices.

Cubic semisymmetric graphs

• load "ImportCubicSSCensus10k.mgm";

  Requires also: CubicSScensus10kplaces.txt and CubicSScensus10k.txt

  Import the database of all cubic semisymmetric graphs on up to 10000 vertices into memory. The following magma function become available:

  • NumberOfCubicSSgraphs(n);

    Returns the number of cubic semisymmetric graphs on order \(n\) vertice, for \(n \le 10000\).

  • CubicSSgraph(n,k);

    Returns the k-th cubic semisymmetric graph on \(n\) vertices.